When I was a physics undergraduate student, I was frustrated by the fact that every measurement was noisy, that every measurement had some uncertainty. Why is it impossible to achieve a perfect measurement? I dreamt of a world without any error bars. Later I learned that variability is actually weaved into the very structure of reality. Think of Heisenberg's uncertainty principle, stating that, on the atomic level, it is fundamentally impossible to know precisely the position and the velocity of a particle. In biology, noise is also everywhere. Even if your measurement is perfect, by chance, two biological entities can be different . Identical twins do not have the same fingerprint. Two bacterial cells can be genetically identical, but behave differently. Is it actually possible to use this variability as a fingerprint to see how the processes in the cell operate? Can we turn the noise into a signal?
Yes, it turns out1. Here, I am sharing a story on how we have used a fluorescent microscopy technique, FRET, in single bacterial cells, to measure random fluctuations in chemosensory array activity, a huge protein complex containing thousands of molecules. These fluctuations reveal the array is poised to a very special point, right on the border between order and disorder.
1. Strange peaks
This story was a long time in the making. It is always challenging to pinpoint precisely when it starts. But in this case, the story started already before this paper, it was on Friday, 9th September 2016. I was on my way to our holiday destination, overlooking a beautiful Swiss lake (Walensee, the banner above this post). Then messages started to pop in2:
In the years before, we had been working hard on measuring the chemotactic pathway activity in single bacterial cells. The chemotaxis pathway is the pathway that bacteria use to navigate their environment. It is basically tapping into the 'brain' of single bacteria. It can also be compared to their sense of smell. It works by means of a FRET probe. FRET (Förster Resonance Energy Transfer) is the physical effect that occurs when two fluorescent dyes come in close proximity, the energy of the one molecule, the donor, is transferred to the other, the acceptor. That means if FRET occurs, the ratio between the donor and acceptor emission signals changes, which can be readily measured using a microscope. In our case, fluorescently labeled molecules were fused to two key proteins in the pathway, that are only interacting when the chemotaxis pathway is active. So, with FRET we were measuring the pathway activity within single bacterial cells.
In the summer of 2016 we were joined by a summer student, Francesca van Tartwijk, who was reading natural sciences at Cambridge (and did very well). We had been chasing critical behavior in cells that had mutant receptors, in which the protein amino acid sequence was modified in only one position. Cells expressing these mutant receptors revealed very slow dynamics in a signal that was averaged over a population of cells and our collaborator Sandy Parkinson had shared them with us to see what was happening on the single cell level. It turned out these mutants did not reveal anything unexpected, so at the end of the experiment I said to Francesca “I am on holiday in Switzerland next week, you understand the method now, so you can measure wildtype as a control”. Wildtype is the name of the normal receptor, "as it occurs in nature". She did, and it turned out the wildtype had the surprises, not the mutants!
The week after I was home and looked again at the time series. Clearly, these peaks were not artefacts. There was a clear anti-parallel signature in the data. As can be seen in the video below, the green donor emission signal went down as the red acceptor went up, and vice versa, causing a clear change in the fluorescence ratio that approximates the FRET signal. An fluorescent artefact such as a wobbling cell typically gives parallel responses (e.g. both channels go up or down). It did not happen in every cell, but in each cell it happened the timing of the switches was different. A sensed strong excitement: what I was seeing were all the chemoreceptors -thousands- seemingly spontaneously and randomly turning off.
I then realised I had seen this behaviour before. When I did experiments on the same type of cells in 2013, in my PhD’s first year, I noticed some bacteria responded with some delay, and others not. At the time, I thought these delays must have been caused by fluctuations of ligand in the flow cell (this is not impossible, but unlikely). But what I noticed was in hindsight actually switching behavior, and because the switches initiate randomly this manifests itself as a delay. If the experiment had continued for longer, I would probably have seen some of the cells switching back. I did not, and I moved on at the time not realising that I had witnessed the same kind of switches.
This makes me think of a quote from Louis Pasteur, the famous microbiologist:
Dans les champs de l‘observation, le hasard ne favorise que les esprits préparés
(in English: during observations, chance favours the prepared mind). Somehow a mind needs to be receptive to see something new. And it requires confidence and intuition in the experimental system to distinguish flukes from really interesting things. A trained pilot can fly an airplane without visual orientation, because they are sufficiently familiar with all the other instrumentation to give them an intuitive model on how the aircraft is behaving without the visual information. So, from this follows a lesson: sometimes you're seeing something wild and spectacular, but it takes confidence and experience to see this is not an artefact!
After doing a repeat of this experiment and seeing the same phenomena, it was time to knock on the door of my doctoral advisor Tom Shimizu, who only took a nanosecond to realise the gravity of the finding.
2. Entire arrays switching on and off
Why is this observation so striking and special? Two state fluctuations are not uncommon in biology. Most famously, ion channels are known to have binary behavior and stochastically switch between an open and a closed state. Also the bacterial flagellar motor switches its rotation (clockwise or counterclockwise). But these are relatively compact assemblies with up to a few dozen units. The chemosensory arrays are much larger, containing thousands of molecules that form one or more clusters associated with the (inner) bacterial cell membrane. Inside these clusters, the receptors are organised as hexagonal arrays together with other signalling molecules (most importantly a histidine kinase). So, a switch in these arrays means that the signal has to propagate through this regular two-dimensional array.
We published the phenomenon of the two-state fluctuations basically because we were afraid others would beat us to it (eLife 2017) but we remained very keen to unravel what was happening precisely. For us, it was quite clear that these fluctuations were caused by a single large chemosensory array flipping on or off. But a sceptic might be unconvinced of this. These switches are only shown when the chemosensory array is brought close to the tipping point. Normally, the chemoreceptor array is far from this transition, but one can add precisely enough chemoattractant to reduce the activity. However, one could suspect that perhaps there are slow fluctuations in this attractant concentration, minuscule, that keeps tipping the system over the edge. Therefore, we endeavoured to find compensatory mutations in chemoreceptors, that would not require ligand stimulation.
Fotios (Fotis) Avgidis joined our lab to work on this task. He started as my masters’ student but soon we worked on this as equal partners. In the wildtype cells, there is a dynamic feedback system that tunes the sensitivity of the receptors, and thereby keeps the activity away from the extremes. We identified two chemoreceptor mutants that also showed intermediate activtity levels, but then in the absence of this dynamic feedback system. One was known, Tar-QEEE (basically one amino acid different compared to how it is usually produced in the cells, the glutamate (Q) at position 311, replacing by glutamine (E)). And we were lucky3 to stumble upon another Tsr-I24K (again a single amino acid replacement, this time at position 214). The fact that we could confirm two-state switching with each of the two receptor species, strengthened the case that this is a property of the array, not specific to a certain chemoreceptor.
Fotis eventually systematically measured all the data and improved the setup with temperature control (the receptor activity is temperature dependent), and over time we added a large number of control experiments, often using mutants that were discovered and provided by Sandy Parkinson. I highlight only the killer experiment here: Fotis simultaneously measured the activity in FRET, as well as how many chemosensory arrays were there. These experiments clearly showing that cells with 1 cluster predominantly show 1 state, while cells with 2 clusters predominantly show multiple states. All of these additional experiments added layers of confidence, like an onion shell around our core finding: entire chemosensory arrays were spontaneously switching on and off.
3. Ising on the cake
What could these fluctuations tell us about how these chemosensory arrays were operating? We wanted to compare these to a model. We chose the two-dimensional Ising model of statistical physics4. While originally developed to describe ferromagnetism, it has been applied in biology, where it is known as conformational spread. It is actually conceptually simple. Consider a lattice of size L by L units. Each unit can adopt two states, on or off. The simplest case is where each unit has no preference to be on or off, but there is an energy penalty depending on the neighbour states J. If J is small, each unit flips independently to generate a salt-and-pepper disordered array. If J is very strong, all units are either on or off permanently and the system is ordered. The Ising model has a critical value J*, which is the value of the phase transition between the disordered and the ordered state. We used code to numerically simulate this process (coded up by Yuval Mulla). These simulations clearly revealed that if J is actually not too far from a critical value J*, the system exhibits two-state fluctuations:
Our objective became clear: by doing simulations with various values of J and L, we hoped to match the fluctuations in the FRET experiments, so potentially we could say something about L and J in the experimental system, and thereby elucidating signalling properties of the system.
However, there were basically two issues. The first issue is that the experiments and simulations could not be directly compared, because they were performed in different units of time. The simulations were in terms of the fundamental switching frequency (ω0) of a single Ising unit, which was unknown. So, we therefore extracted two timescales from the experimental and simulated time series, the time between switches, and the time it takes to flip. This ratio between these timescales can directly be compared.
The second problem was more difficult. In principle, there were many combinations of J and L that yielded the same timescale ratio. So, it was not clear how we could say anything about either L or J. However, there is one really important effect, which is called finite-size scaling. As discovered in the 1970's, the value of J* that separates the ordered from the disordered state actually depends on L (with smaller L requiring larger J*).
In the summer of 2019, I took a piece of paper and sketched the phase diagram, to see how far we would get in constraining the the lattice size L, the coupling energy J and the frequency ω0. I had used values of L=10 to L=30, mostly because the simulations became quite slow for higher numbers. Then, when I just divided the values of J by J* for that given size, to my surprise I noticed that all values were actually very close to J*, regardless of the uncertainty in L:
(note in the below picture of that note, I use N where the paper uses L, and I use E=8J).
So, despite uncertainty in L, J had to be close to J* to explain the data. And from the uncertainty in L, we could then provide a range of ω0. Later Tom then thought of a clever way to constrain L based on the fact that we know there are about 10,000 chemoreceptor molecules per cell, and these are ordered in either core unit (12 molecules per core unit, meaning about 1000 core units) or a unit cell (36 molecules per unit, hence 277 core units). Hence L=17 and L=30 seemed a reasonable range. It did not affect our estimate of J, but it did further constrain our estimate of ω0.
This is the main result of this paper. The finite scaling analysis yields a strongly confined J, namely to be within a few percent of J*. So, in other words, these chemosensory arrays are close to the Ising phase transition, or to criticality. They operate right on the border between order and disorder.
4. Why would E. coli care about criticality?
As a physicist, I find the idea of criticality immediately exciting. There have been other collective systems in biology that are thought to organise themselves close to a critical point, from populations of cells, bird flocks and even the human brain. Perhaps criticality doesn't excite you. There is no accounting for tastes, as the English say. This doesn't mean we cannot quarrell about it, it it just means I cannot rationally force you to. But the really important question here is why E. coli would care about criticality. As we can assume that the motile and chemotactic behavior has been subject to evolutionary pressures, why did the system end up in this specific point of space?
We performed experiments and simulations to show that while increased lattice interactions increases the cooperativity of the response, and thereby allows cells to amplify signals, it also decreases its response time. This response time actually decreases dramatically after J exceeds J*, an effect that is called critical slowing down. Interestingly, J being close to J* maximises their amplification before the system becomes so slow it cannot respond adequately.
But of course it may not be always optimal to be close to criticality. It also enhances the sensitivity to noise. It seems that E coli can also tune the distance to criticality. One way is by expressing different receptors. E coli has five different chemoreceptor species, but it does not express all of them in equal amounts. There are conditions where E. coli mostly produces a serine receptor Tsr (likely because it assumes that its main task is going to be to chase a serine gradient), but in other growth conditions it produces a mixture of Tsr and Tar (the aspartate receptor), clearly evidently trying to mix signals. When a cell produces such a mixture of teceptors in the same array, the cooperativity to these signals goes down and effectively this means the cell moves away from criticality!
The switching statistics of binary switches in pathway activity revealed that the coupling energy J between the same kind of receptors is close to the critical value. Wildtype E. coli cells, however, do not switch activity in this binary fashion. This would not be compatible with functioning chemotaxis. One reason for this difference is the receptor mixing, mentioned above, and another reason is the presence of the adaptation system (that in itself is also a source of noise). But the fluctuations in pathway activity do not disappear in wildtype cells. The binary switches are transformed into continuous fluctuations that can be as high as 80% of the mean value:
This may be surprising for a signalling system, but it has actually been predicted theoretically that noise in pathway activity can actually increase the performance in strongly heterogeneous environments, where gradients only exist locally. In such environment, the performance of the search process not only depends on chasing the gradient, but also by random exploration that enhances the chance of encountering a gradient in the first place. Hence, this signalling system is not only about the transfer of information from outside of to inside of the cell, but seems to have an important function in generating signals, that enhance exploration, in case the environment remains silent!
5. The future
Since we placed our work on the archive a few years ago, the stochastic two-state switching has already inspired others to work on different models to explain the data, with one key advance being that the models do not assume an equilibrium model (as our standard Ising model is) but instead have a model that explicitly includes dissipation in the chemosensory arrays. These models can actually explain one difference between the model and our data that we could not explain (it is the asymmetry that the cells switch slightly faster going up in activity compared to going down) 5. It has been very rewarding to see these developments and we hope that our improved understanding on this system will also provide insights and inspiration for other protein complexes, of which there are many across cell biology.
I've highlighted a few things here that I found very memorable about this journey, but evidently over an 8 year timeline many more stories have accumulated for which I lack the space. I am grateful to everyone who helped bringing this work to the light of day, and I congratulate all team members: Fotis, Tom, Sandy, Yuval and Evan with this great result. I am very grateful.
Footnotes
1) Actually, there are many examples of noise being turned into a method to extract information. There is a technique based on this principle, fluorescence correlation microscopy. And people have used gene expression noise to understand gene regulation, just to name a few examples.
2) I'm recreating this chat here, that paraphrases a longer conversation between me and Francesca, in Dutch.
3) We later discovered that we could have used Tsr [EEEE], quite analogous to Tar. Finding alternative mutations is indeed a lucky strike. For a protein that is 500 amino acids long, there are nearly 10,000 possible single amino acid substitutions!
4) By the way, many Americans say Ising as in “icing”. My section title is a little mean as it invites that pronounciation. But as Ernst Ising was German, and the initial publication was in German, it would be more appropriate to pronounce it the German way ("Esing"). It is also one of the few models that has been named after the student, and not the professor!
5) You can read more about this here: a paper (by Hathcock, Yu & Tu) and a blog post from the authors, and another exciting preprint (by Sherry and colleagues).